Markus Kirchweger | AC Group | TU Wien

Formally Verified Graph Generation with SAT Modulo Symmetries and Lean

Thu, 01 Jan 2026 00:00:00 +0000

Graph Choosability via SAT: Beyond the Nullstellensatz

Thu, 01 Jan 2026 00:00:00 +0000

Smart Cubing for Graph Search: A Comparative Study

Thu, 01 Jan 2026 00:00:00 +0000

Breaking Symmetries in Quantified Graph Search: A Comparative Study

Wed, 01 Jan 2025 00:00:00 +0000

ASK-SAT: Alternating Symmetry-Breaking Combinatorial Search with SAT

Mon, 01 Jan 2024 00:00:00 +0000

Project Acronym: ASK-SAT (Alternating Symmetry-Breaking Combinatorial Search with SAT)

Funding organization: Austrian Science Fund (FWF)

Project number: P 36688

Grant DOI: 10.55776/P36688

Project Team

Topic

Many unsolved problems in discrete mathematics and extremal combinatorics can be stated as whether a combinatorial object with a particular property and size exists.

The project focuses on developing novel methods for answering such questions using the innovative Satisfiability Modulo Symmetries (SMS) technique. This approach departs from traditional exhaustive search strategies by dynamically identifying and excluding redundant sub-configurations, thus streamlining the search process while utilizing the power of solvers for the propositional satisfiability problem (SAT).

The project aims to extend the capabilities of SMS to effectively tackle the existence of objects whose defining property requires alternating quantifiers, which present unique challenges beyond the scope of conventional SAT methods. This involves integrating advanced computational tools, including quantified Boolean formulas and symmetry-reasoning technologies.

Through this research, the project aspires to advance the fields of automated reasoning and discrete mathematics.

Software

The software tool developed through the project is available via GitHub, the documentation via Read the Docs.

Computing small Rainbow Cycle Numbers with SAT modulo Symmetries

Mon, 01 Jan 2024 00:00:00 +0000

SAT Modulo Symmetries for Graph Generation and Enumeration

Mon, 01 Jan 2024 00:00:00 +0000

Satisfiability Modulo User Propagators

Mon, 01 Jan 2024 00:00:00 +0000

A SAT Solver's Opinion on the Erdős-Faber-Lovász Conjecture

Sun, 01 Jan 2023 00:00:00 +0000

Co-Certificate Learning with SAT Modulo Symmetries

Sun, 01 Jan 2023 00:00:00 +0000

IPASIR-UP: User Propagators for CDCL

Sun, 01 Jan 2023 00:00:00 +0000

SAT-Based Generation of Planar Graphs

Sun, 01 Jan 2023 00:00:00 +0000

A Beam Search for the Shortest Common Supersequence Problem Guided by an Approximate Expected Length Calculation

Sat, 01 Jan 2022 00:00:00 +0000

A Beam Search for the Shortest Common Supersequence Problem Guided by an Approximate Expected Length Calculation

Sat, 01 Jan 2022 00:00:00 +0000

A SAT Attack on Rota’s Basis Conjecture

Sat, 01 Jan 2022 00:00:00 +0000

SAT Modulo Symmetries for Graph Generation

Fri, 01 Jan 2021 00:00:00 +0000